28-12-2012, 06:07 PM
Baseband Digital Transmission
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OBJECTIVES
This experiment investigates how a digital data stream can be encoded into a sequence of pulses
for transmission through a baseband analog channel. Specifically, you will examine:
• various line coding methods used for digital baseband modulation in data communication
applications;
• spectral properties of those lines codes, i.e. their power spectral densities;
• two important causes of signal distortion in a data communication channel: additive gaussian
noise and filtering effects due to the bandwidth of the channel;
• effects of intersymbol interference (ISI) and additive noise as observed with the help of
the eye pattern.
PROCEDURE
1. Line codes for binary signaling over baseband channels
Binary digits produced by a data source can be serially encoded using a variety of signaling formats
called line codes for transmission over an analog baseband channel. Their structure and spectral
properties will be examined in this section. You will be using the modul custom Matlab command: where Fd is the data rate in symbols per second (bauds) and Fs is the simulation sampling frequency.
Note that in this experiment we are only concerned with binary sequences and binary modulation
schemes. Therefore, Fd corresponds to the binary data rate in bits per second (b/s). The action of the
command is to take the vector binary_sequence and modulate it according to the specified line
code. The following codes are supported: ‘unipolar_nrz’, ‘bipolar_nrz’, ‘bipolar_rz’, ‘ami’,
‘manchester’, ‘miller’, ‘unipolar_nyquist’, ‘bipolar_nyquist’, ‘raised_cosine’ and ‘duobinary’.
Many of the custom Matlab commands (scope, modul etc.) require the Fd and Fs parameters.
However, if they are defined as global variables before these commands are executed, then Fd and Fs
do not need to be passed as parameters (see 1.1 below for an example).
Simulating a baseband channel with noise
You will now simulate the characteristics of an ideal baseband communication channel including
additive white Gaussian noise. The channel is modelled as an ideal low-pass filter whose output is
summed with the output of a white Gaussian noise generator (see conceptual diagram of Figure 1).
This channel model is implemented as the custom Matlab function bbchannel: Again, if the simulation sampling frequency Fs has been apriori defined as a global variable, it
need not be passed as a parameter.
A computationally efficient implementation of the low-pass filter requires the Signal Processing
Toolbox, not included with the student edition of Matlab. For users of the student edition, a simplified
filter design technique is employed for which you have to set the MATLAB_SE global variable.
Eye pattern
The distortion effects introduced by the channel and noise can be visually inspected by observing
the eye pattern (also referred to as eye diagram) of the ouptut waveform. The eye pattern can be
observed with an oscilloscope where multiple sweeps are superimposed on top of one another. The
sweeps are triggered by a clock signal synchronized to the data rate which can be provided externally
or derived from the channel output itself. Because a large number of sweeps are overlaid, the eye pattern
is a good visual aid to observe the average and the worst-case behavior of the output waveform.
Its appearance is that of a circular or somewhat rectangular opening (the eye) between the traces.
Pulse shaping and ISI
Channels with a bandwidth smaller than the nominal bandwidth of the signal, as well as channels
with non-flat spectra (e.g. a notch in the middle of the useful band) can cause significant time
spreading of the signal. If the time spreading is larger than the symbol duration, it results in intersymbol
interference (denoted as ISI). If we consider one transmitted symbol (pulse) in isolation, ISI refers
to the distortion caused by the fraction of energy from other pulses in its vicinity which has been projected
onto the desired symbol by the time spread in the channel. This section illustrates how shaping
the pulses prior to transmission via a transmit filter can affect the amount of ISI at the receiver.
POST-LAB QUESTIONS
1. Which line codes will generate a waveform with no DC component regardless of the binary
sequence represented? Why is it sometimes important in practice to encode signals for transmission
in such a way as to have no DC component?
2. At the output of a channel, it is necessary to extract a symbol-rate clock synchronized with the
received signal. Such a clock signal indicates when a specific symbol starts and can therefore be
used to trigger sampling of each received symbol. This operation, termed timing recovery is facilitated
by some line codes. Which ones? Why? Hint: start by looking at the problem when the message
to be transmitted is all ones or all zeros.
3. Given a baseband data communications channel with a usable bandwidth of 10 kHz, what is the
maximum data rate sustainable for each of the line codes examined in this experiment? (Refer to
part 1 in the Procedure.)
4. Keeping in mind that the channel noise is additive and uncorrelated with the channel input, derive
an expression for the PSD of the channel output in terms of the input and noise PSDs.
5. In tables 2 and 3, compare the eye patterns obtained with noise power of 0.01 W and bandwidth of
1000 Hz. For which line code do you observe the best eye diagram? Explain this result in terms of
the properties of line codes and the channel.